Spring 2013

**ECMA Student/Faculty Picnic: Tuesday, April 30 4:00 pm -?? **

Economics/Mathematics PICNIC

**Location: Olin Quad (if Rain – OLIN 383).**

**Pi Mu Initiation Ceremony and Banquet: Thursday, April 18, 2013 at 5:00 pm in the Refectory **

**2013 Initiates: **Seniors: Rebekka Olandt and Bonnie Reiff

Juniors: John Fowler and Katherine Perez

Sophmores: Margo Boyd, Daniel Steinberg, and Cody Stockdale

Distinguished Visiting Professor Lecture: Thursday, April 18 at 4:00 pm in 254 Olin Science

Department of Mathematics and Statistics

University of Vermont

**Abstract: **Given an integral positive definite quadratic form Q, the generating series which records the number of representations of an integer n = Q(x) is a modular form: the series transforms nicely under certain change of variables. The connection between such arithmetically-deﬁned counting functions and modular forms is one piece of the Langlands philosophy, which predicts deep connections between representations of classical groups and modular forms in different guises via associated Galois representations. In this talk, we consider algorithms for computing systems of Hecke eigenvalues for classical groups in the language of algebraic modular forms, as introduced by Gross. This is joint work with Matthew Greenberg.

Student Colloquium Series: Thursday, April 18 at 12:00 pm in 268 Olin Science

Mathematics Department

Bucknell University

**Abstract: **How might one try to find out about the rate of marital infidelity 2000 years ago? Is there an technique which covers both thinking about gambling and also competition between the red and grey squirrel in Great Britain? With the aid of Markov chains, a surprisingly accessible tool, we'll consider all of these problems, meeting along the way what the speaker thinks is the most intriguing journal article title ever invented (and the runner-up).

**PIZZA/CALZONES and DRINKS provided.**

Distinguished Visiting Professor Colloquium: Tuesday, April 16 at 10:00 am in 372 Olin Science

Department of Mathematics and Statistics

University of Vermont

**Abstract: **In 1966, Mark Kac asked in the American Mathematical Monthly, "Can one hear the shape of a drum?" In other words, can you determine the shape of a drumhead from the sound that it makes, the list of its basic harmonics? The answer to this question is "no": in 1992, Gordon, Webb, and Wolpert constructed, using a method of Sunada, a pair of regions in the plane that have different shapes but identical eigenvalues.

Many variations of this problem have been considered. In 1980, Vigneras proved the existence of compact surfaces with negative curvature--we might think of them as vibrating donuts--which have the same spectrum (overtones) but are not isometric. However, her pair of examples (when a mistake was corrected) had genus 100801.In joint work with Peter Doyle and Ben Linowitz, we exhibit a pair of genus 6 surfaces and a pair of "pinched" spheres (genus 0 orbifolds) which have the minimal hyperbolic volume among all such arithmetic examples.

Distinguished Visiting Professor Lecture: Thursday, April 11 at 9:00 am in 105C in the Biology Building

School of Mathematics

University of Leeds

**Abstract: **We give embedding theorems for a very general class of weighted Bergman spaces called Zen spaces: the results include many of the classical Carleson embedding theorems as special cases.

Next, a study is made of Carleson embeddings in the right half-plane, induced by taking the Laplace transform of functions defined on the positive half-line (these embeddings have applications in control theory): particular attention is given to the case of a sectorial measure, and complete necessary and sufficient conditions for a bounded embedding are given in many cases.

--- Joint work with Birgit Jacob and Sandra Pott

Distinguished Visiting Professor Lecture: Tuesday, April 9 at 4:00 pm in 372 Olin Science

School of Mathematics

University of Leeds

**Abstract: **In the 1920s Denjoy and Carleman investigated whether two positive measures on the real axis were necessarily the same if their moments (integrals of powers of x) were equal. The answer is yes, but only if the moments do not grow too quickly. The question is linked to another, more elementary question: if all the derivatives at the origin of a smooth function are 0, when is it necessarily the zero function?

We look at natural extensions of these questions. For example, if the nth moments differ by O(C^n) and do not grow too quickly, then the measures can only differ on [-C,C]. After this, we give extensions to R^N, and applications to the theory of bases and sampling. The only tools used are techniques from elementary complex analysis.

--- Joint work with Isabelle Chalendar, Laurent Habsieger and Tom Ransford.

Distinguished Visiting Professor Faculty Colloquium: Tuesday, April 9 at 10:00 am in 351 Olin Science

Département de Mathématiques, Université Lyon I

**Abstract: **An inner function is a bounded analytic function on the unit disk whose radial limits have modulus one at almost every point of the unit circle. Due to classical results of A. Beurling and others, inner functions have a crucial role in the theory of Hardy spaces and the operators acting on them. The problem of when there is a non-trivial “factoring” of an inner function as the composition of other inner functions was introduced by K. Stephenson 30 years ago. An inner function is called prime if in any such composition one of the factors is a MÖbius transformation, and semiprime if a factor must be a finite Blaschke product. In this work we study when inner functions formed from various classes Blaschke products are prime or semiprime.

We show that prime finite Blaschke products are dense in the set of all finite Blaschke products and thus weak-* dense in the set of all inner functions. We also prove that finite products of thin Blaschke products can be uniformly approximated by prime Blaschke products.

This is a joint work with P. Gorkin and J. R. Partington.

Distinguished Visiting Professor Lecture: Monday, April 8 at 4:00 pm in 372 Olin Science

Département de Mathématiques, Université Lyon I

**Abstract: **There is an outstanding problem in operator theory, the so-called “Invariant Subspace Problem", which has been open for more than a half of century. There have been significant achievements on occasions, sometimes after an interval of more than decade, but its solution seems nowhere in sight. The invariant subspace problem for a complex Banach space X of dimension at least 2 is the question whether every bounded linear operator T : X → X has a nontrivial closed T-invariant subspace (a closed linear subspace M of X which is different from {0} and X such that T(M) M).

For the most important case of Hilbert spaces H the problem is still open, though Eno and Read showed that the invariant subspace problem is false for some Banach spaces.

There have been many significant developments in this branch of operator theory.Therefore, it was necessary to be selective in our choice of material. Some themes to be discussed include Compact operators and their generalizations, namely, finitely strictly singular operators and strictly singular operators, as well as universal operators, and the study of composition operators and their invariant subspaces, as key examples.

This talk is based on the book *Modern Approaches to the Invariant Subspace Problem* by I. Chalendar and J.R. Partington, Cambridge University Press, 2011.

Student Colloquium Series: Thursday, April 4 at noon in 268 Olin Science

Economics Department

Bucknell University

**Abstract: **We live in a world where data is abundant, and increasingly being used by political campaigns, corporations, and other institutions to make decisions, influence our choices, tailor marketing materials to individual consumers, and increase our understanding of the world. However, data can be misused, misleading, and messy. Professor Amy Wolaver will discuss some of the pitfalls to avoid when analyzing data. She will also discuss how economics and applied statistical analysis can be used to avoid those pitfalls and help identify social problems, test theories about behavior, and help shape good public policy responses.

**PIZZA/CALZONES and DRINKS** provided.

Distinguished Visiting Professor Seminar: Wednesday, March 27, 4:00 pm in 372 Olin Science

Associate Professor of Mathematics

University of Maine, Farmington

**Abstract: **In this talk, we will compute the Bieri-Neumann-Strebel geometric invariant Σ^1 of the pure braid group on n strands. We will begin with a brief discussion of the Σ-invariant and of the pure braid groups Pn . In particular, we will use the presentation for P_n introduced by McCammond and Margalit. We will then discuss the techniques used to compute Σ^1 (P_n ) and give the computation. This is joint work with John Meier and Jon McCammond.

Distinguished Visiting Professor Colloquium: Tuesday, March 26, 4:00 pm in 372 Olin Science

Associate Professor of Mathematics

University of Maine, Farmington

**Abstract: **In 1987, Bieri, Neumann, and Strebel introduced the geometric invariant Σ of a group. This invariant detects, among other things, whether a normal subgroup with abelian quotient is ﬁnitely generated or not. The theory that has accompanied this invariant has been rich, but the invariant has proven rather diﬃcult to compute. In this talk, we will deﬁne this invariant, compute (hopefully) lots of examples, and discuss some techniques that have been used in the computation of certain groups. Time permitting, we will also discuss some analogous invariants that have been developed over the years since the BNS invariant was introduced.

Student Colloquium Series: Thursday, February 28 at noon in 268 Olin Science

Mathematics Department

Bucknell University

**Abstract: **One of the more recent contributions to the field of statistics in the area known as clustering. Clustering has come out of the need to analyze large data sets. Specifically, clustering is a technique that looks for common types of individuals from within the entire collection of data. In this talk, we will examine some of the more commonly used clustering methods, such as hierarchical clustering, k-means clustering and model-based clustering. I will then discuss a clustering algorithm for longitudinal data, and introduce my method for clustering these types of trajectories while taking into account potentially informative missing values.

**PIZZA/CALZONES and DRINKS** provided.

Student Colloquium Series: Thursday, February 14 at noon in 268 Olin Science

Technical Specialist at

Computer Support Services, Inc., Lewisburg

**Abstract: **During your mathematical studies, do you sometimes wonder, "Where will I ever use this stuff”? I recall asking this same question many times. However, after considering my varied career endeavors (from teaching to aerospace to developing applications for companies like Mack Trucks), I’ve found that mathematics has assisted me in solving a wide-range of problems, and even opened some doors along the way. Playing poker? Well, that helped too.

*I look forward to discussing how I’ve applied mathematics in my career and considering if and how it will help you too.*

**PIZZA/CALZONES and DRINKS** provided.

Student Colloquium Series: Thursday, January 31 at noon in 268 Olin Science

Bucknell University

Civil and Environmental Engineering Department

**Abstract: **Because the behavior of building structures in earthquakes is highly non-linear and difficult to predict, modern seismic design still relies heavily on several fundamental concepts from undergraduate-level physics, differential equations and linear algebra. This talk will introduce mathematical models used in seismic design and discuss the relationship between the ideal (mathematics) and the real (buildings). Concepts will be demonstrated using physical models as well as results from current experimental and computational research on earthquake-resistant design of structures.

*All students are very welcome to attend.*

**PIZZA/CALZONES and DRINKS** provided.

Student Colloquium Series: Thursday, November 15 at noon in 268 Olin Science

Bucknell University

Department of Mathematics

**Abstract: **One hundred years ago, Max Dehn (1878-1952) first articulated the three fundamental problems in Combinatorial Group Theory. Dehn predicted that these problems would prove difficult, and that their solutions would require a "penetrating study of the subject". In this talk we shall consider one of these problems, The Word Problem. We will introduce groups, describe The Word Problem, and give an account of the famous solution to the problem. Throughout will see see how asking just the right questions can shape a field of study.

*All students are very welcome to attend.*

**PIZZA/CALZONES and DRINKS** provided.

Distinguished Visiting Professor Seminar: Thursday, November 1, 4:00 pm in 351 Olin Science

Senior Lecturer in Pure Mathematics

School of Mathematics and Statistics

University of St Andrews

**Abstract: **I'll describe some current work-in-progress with Burdges, Linton, Neunhoeffer and Parker. We are using geometric ideas from small cancellation theory to develop a new class of practical algorithms for working with finitely-presented groups, and other algebraic structures. Amongst other applications, we solve the word problem in a wide variety of finitely-presented string-rewriting structures, including various types of group presentation.

Distinguished Visiting Professor Colloquium: Tuesday, October 30, 4:00 pm in 351 Olin Science

Senior Lecturer in Pure Mathematics

School of Mathematics and Statistics

University of St Andrews

**Abstract: **Let G be a finite group, and let S be a subset of G. We say that S generates G if it is possible to make every element of G by repeatedly multiplying together elements of S, and their inverses. We write d(G) to denote the smallest number of elements necessary to generate G. The talk will start by surveying some old and new results on upper bounds for d(G). For example, we could be given information about the structure of G, or told that G can be represented as a group of n x n matrices, or as a group of permutations of the numbers 1,…, n. We will then move on to thinking about the probability that a random set of d elements of G generates G. I'll present a beautiful theorem due to Liebeck and Shalev, describing what happens asymptotically when G is a finite simple group, and go on to some recent work which adds some numerical understanding to this picture. Connections between minimal and random generation will finish off the talk.

Student Colloquium Series: Thursday, November 1 at noon in 268 Olin Science

Meridith Joyce ’13, Ben Sokolowsky ’13,

Jessica Morra ’14, Kasey Segiel ’14, Meng Yang ’14

**Abstract: **Do you want to know about summer options for undergraduates with mathematical interests? Five students will share information about the research experiences and internships they had last summer, providing practical information, opinions, and advice for you!

*All students are very welcome to attend.*

**PIZZA/ CALZONES and DRINKS** provided.

Student Colloquium Series: Thursday, October 18 at noon in 268 Olin Science

Carnegie Mellon University

Department of Statistics

**Abstract: **In a 2009 interview, Hal Varian, the chief economist at Google, stated that "the sexy job in the next ten years will be statisticians". In this talk, I want to discuss this claim and offer some insight into why it is true. I'll talk about the role of statistics in the modern world and some of the resultant career possibilities for statisticians. Along the way, I'll also describe my background and path to becoming a statistician. Finally, I'll briefly outline some of the wide-ranging projects with which I am currently or have been involved, including those in genetics, cognitive psychology and market segmentation.

*All students are very welcome to attend.*

**PIZZA/ CALZONES and DRINKS** provided.

Distinguished Visiting Professor Seminar: Friday, October 5, 12:00 pm in 351 Olin Science

Associate Teaching Professor

Department of Statistics, Carnegie Mellon University

**Abstract: **The United States Patent and Trademark Office has over 8 million patents. While the patents have all been uniquely identified, the inventors and assignees have not, making it difficult/impossible to study technology and innovation entrepreneurship via patenting trends, a common practice in public policy research. For example, is Dave Miller who patented in San Francisco in 1999 the same person as David Miller who patented in Palo Alto in 2000? What about David A. Miller in San Jose in 2001? This record linkage problem requires developing statistical text analysis methods to determine the patents for each unique inventor. Using a set of 47,125 labeled optoelectronic inventor records, we evaluate the performance of several existing ad-hoc inventor disambiguation algorithms and show, by comparison, that a more statistically-driven approach substantially reduces the percentage of false positive and false negative errors. In particular, we introduce a Forest of Random Forests, a procedure that conditions on features of our records to further improve the disambiguation and make seemingly computational intractable problems feasible.

Distinguished Visiting Professor Colloquium: Wednesday, October 3, 4:00 pm in 351 Olin Science

Associate Teaching Professor

Department of Statistics, Carnegie Mellon University

**Abstract: **There has been a recent increase in the use of cognitive or intelligent tutoring systems in the classroom. The Assistment Project is a web-based tutoring program jointly developed by Carnegie Mellon University, Carnegie Learning, and Worcester Polytechnic Institute that blends tutoring "assistance" with "assessment" reporting. Over 4000 students in Massachusetts and Pittsburgh used the system in 2007-2008. In this talk, I will describe the tutor and the feedback it provides through both simple summaries and statistical modeling. With the high-dimensional data (students, skills, questions) that these types of tutors provide comes a host of estimation challenges not yet met by standard psychometric models. As an alternative, we incorporate clustering and visualization methodology to generate real-time practice feedback for the classroom. I will compare this high-dimensional approach to more traditional psychometric methods and discuss its advantages and disadvantages.

Student Colloquium Series: Thursday, October 4 at noon in 268 Olin Science

Program Officer, Division of Undergraduate Education, National Science Foundation

**Abstract: **"From calculus we know that a derivative of a function can be approximated using a difference quotient. There are different forms of the difference quotient, such as the forward difference quotient (most common), backward difference and centered difference. I will introduce and discuss "Mickens differences," which are decidedly different differences that can be used to approximate derivatives. Professor Ronald Mickens is an African American Physics Professor at Clark Atlanta University who has published almost 200 peer-reviewed articles on this and related topics. These nonstandard finite differences (i.e. NSFD, as they are more commonly known) can produce discrete solutions to a wide variety of differential equations with improved accuracy over standard numerical techniques. Applications drawn from first-semester Calculus to advanced computational fluid dynamics will be given.

*All students are very welcome to attend. Knowledge of elementary derivatives/anti-derivatives and Taylor Approximations will be assumed.*

**PIZZA/ CALZONES and DRINKS** provided.

Student Colloquium Series: Thursday, September 20 at noon in 268 Olin Science

Mathematics Department – Bucknell University

**Abstract: **Anyone who has taught mathematical enrichment in High School probably has brought in a pine cone or a picture of a sunflower and pointed out the Fibonacci sequence hiding in the spirals waiting to be discovered. We will talk about how this ubiquitous sequence worms its way into nature. The talk is based on the article “Dancing Elves and a Flower’s View of Euclid’s Algorithm” by Susan Goldstine which appeared in the winter edition of the Mathematical Intelligencer in 2006.

**PIZZA/ CALZONES and DRINKS** provided. All are welcome.

Student Colloquium Series: Thursday, September 6 at noon in 268 Olin Science

History, Intuition, Pedagogy, Proof.

Distinguished Teaching Professor Emeritus At West Point

**Abstract: **The Fundamental Theorem of Calculus (FTC) was a theorem with Newton and Leibniz, a triviality with Bernoulli and Euler, and only took on the meaning of "fundamental" when Cauchy and Riemann defined the integral. FTC became part of research mathematics in the 19th century, but waited until the 20th century to take hold in classroom mathematics. We will discuss the transition from clear intuition to rigorous proof that occurred over three centuries. Most importantly, we shall explain why both parts of the FTC are vital.

**PIZZA and DRINKS** provided. All are welcome.

Distinguished Visiting Professor Seminar: Wednesday, September 5, 4:00 pm in 371 Olin Science

Department of Mathematics

University of Georgia

**Abstract.** Let A and B be subsets of an abelian group. One of the main endeavors of additive combinatorics is to answer questions of the following type: If A and B are 'large', what can one say about the structure of the sumset A + B? In the setting of the integers, a good measure of the amount of additive structure in a given finite set is provided by the size of the longest arithmetic progression one can find in the set.

In this talk we will discuss Croot, Laba and Sisask's probabilistic approach to finding L^p-almost-periods of convolutions and present their very short proof of a theorem of Ben Green on the existence of long arithmetic progressions in sumsets.

Distinguished Visiting Professor Colloquium: Tuesday, September 4, 4:00 pm in 351 Olin Science

Department of Mathematics

University of Georgia

**Abstract.** Additive combinatorics is a rapidly developing area of mathematics with close connections to number theory, combinatorics, harmonic analysis, and ergodic theory that includes many beautiful results such as Szemeredi's theorem and the Green-Tao theorem on long arithmetic progressions in the primes.

In 1975, Szemeredi proved that every set of integers of positive density must necessarily contain arbitrary long arithmetic progression, thus settling a 1936 conjecture of Erdos and Turan. The original proof of this result is legendarily difficult, but aside from its importance the paper led to one of the most important ideas in graph theory, the Szemeredi regularity lemma. Remarkably, there have been several subsequent proofs of Szemeredi’s theorem, and it would scarcely be an exaggeration to say that each of them has opened up an entirely new field of study. In 1977 Furstenberg proved the result by an ergodic- theoretic approach. In 1998 Gowers received the Fields' medal for the third known proof of this theorem, using a kind of “higher Fourier analysis” (generalizing the pioneering work of Roth on arithmetic progressions of length three from 1953) to obtain the first sensible quantitative bounds for this problem in the case of progressions of length greater than three. In this talk we shall discuss the history of Szemeredi's theorem, but will ultimately focus most of our attention on quantitative issues and Gowers' generalization of the beautiful Fourier-analytic argument of Roth.

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